Collimator optimization for detection and quantitation tasks: Application to gallium-67 imaging

We describe a new approach to the problem of collimator optimization in nuclear medicine; our methodology is illustrated for the challenging case of gallium-67 imaging. Collimator-design methods based on empirical rules, such as specification of an allowable level of single-septal penetration (SSP) at a fixed energy, are especially inappropriate for radionuclides characterized by an abundance of high-energy contaminant photons that scatter in the patient, collimator, and/or detector before detection within one of a few photopeak energy windows. Lead X-rays produced in the collimator are an additional source of contamination. We designed optimal collimation for Ga-67 based on relevant clinical imaging tasks and a realistic simulation of photon transport in a phantom, collimator, and detector. Collimator designs were compared on the basis of performance in lesion detection, as predicted by a three-channel Hotelling observer (CHO), as well as in tumor and background activity estimation (EST), quantified by task-specific signal-to-noise ratios (SNRs). The optimal values of collimator lead content were 22.0 and 23.8 g/cm(2), respectively, for CHO and EST, while the optimal geometric resolution values were 1.8 and 1.6 cm full-width at half-maximum (FWHM), respectively, at a distance of 23.5 cm. The resolution of a commercially available medium-energy low-penetration collimator (MELP) is 1.9 cm FWHM at this distance. The optimal values for SSP at 300 keV were 7.3% and 5.8% based on CHO and EST, respectively, compared to 5.2% for the MELP collimator. Compared with the commercial MELP collimator, the Ga-67 collimator optimized for tumor detection or activity estimation tasks provided improved geometric spatial resolution with reduced geometric efficiency and, surprisingly, allowed an increased level of single-septal penetration.